Have you wondered why do we say we can't know about two physical quantities at the same time in quantum mechanics? Do you know which experiment first created this question among the researchers?
In chapter 6 of my blog in Stern Gerlach experiment I stated about single stage SG experiment, that is the experiment consisted of only one inhomogenous magnetic field which splitted the silver atom in one specific direction. In this chapter, we are going to see about the experimental conclusion by setting up multiple inhomogenous magnetic field. It is called as sequential Stern-Gerlach experiment.
From fig a it is clear that the SGz stands for an apparatus with the inhomogenous magnetic field in the z direction. We then block the SZ- component out of the 1st apparatus and let the remaining Sz+ component be subjected to another SGz apparatus. You will see that this time there is only one beam component coming out of the 2nd apparatus, just the Sz+ component. This is not surpising at all; after all initially if the atom spins are up, they are expected to remain so, regardless of any external field that rotates the spins between 1st and 2nd apparatus.
In fig b, you will see a different result from before. The 1st SG apparatus is same as before but the 2nd one (SGx) has an inhomogenous magnetic field in x direction. SGz that enters the 2nd apparatus is now split into Sx+ and Sx- component with equal intensities. It should not happen logically. Unlike in the previous case the spin direction remained same throughout the apparatus, this time it got changed. After passing Sz+ component in SGx apparatus, it splits the atom in Sx+ and Sx- direction.
In fig c, the setup of the experiment and result is same till SGx apparatus. After the beam is passed through this apparatus, Sx- beam is blocked and only the Sx+ beam is passed through the SGz apparatus and then we got Sz+ and Sz- beam. Now the question arises, why did we setup the 3rd apparatus here? The answer is that after selecting Sx+ beam in the 2nd apparatus completely destroyed the previous information about Sz. So to regain the previous information about SGz, the 3rd apparatus was used. This proves that we can't know simultaneously about Sx and Sz component spin at the same time. So, here again the topic comes about time, which I have discussed about it in chapter 7.
Now here are the questions for the readers, is there any classical or quantum or both classical and quantum single experiment which shows exactly the same result as with the above experiment? How can you relate time which I have discussed in chapter 6 with this experiment because the experiment shows that we can't know about two spin components at the same time. What is your perspective of time? Share your answers through the comments, social media links that I have attached.
